The problems of peptide identification and protein identification are of fundamental importance in proteomics. We propose to study a new multi-pronged framework for the de novo peptide sequencing and protein identification under uncertainty problems using tandem mass spectroscopy. The proposed approach will be based on fundamental advances in mathematical modeling via mixed integer optimization, as well as theory and algorithms for optimization under uncertainty. We expect that significant advances will be introduced in theory and algorithmic enhancements. We put forward the following four specific aims: Specific Aim 1: Investigate and develop a novel de novo computational approach for the peptide identification based on information of the ion peaks in the peptide spectrum and a mixed-integer optimization modeling and algorithmic framework. Specific Aim 2: Investigate novel de novo methods for the identification of peptides in complex protein mixtures which will account for experimental uncertainty in the calculation of the mass/charge ratios of the ion peaks. Specific Aim 3: Study and develop a new hybrid in silico method which will combine the de novo approach of Specific Aim 1 with database methods for the peptide identification. Specific Aim 4: Investigate and develop a new approach for the protein identification which will combine the advances in Specific Aims 1-3 with database homology based methods. Preliminary studies are reported in Specific Aims 1, 2, and 3 (sections C.1, C.2, D.1, D.2, D.3), and the results, via comparative studies and computational efficiency, demonstrate the potential of the proposed research for high throughput peptide and protein identification.